An activist investor wants the parent of Ann Taylor to get off the discount rack and sell itself for full price.

Engine Capital LP, which along with a partner controls more than 1% of Ann Inc. stock, believes a strategic or private-equity buyer would be willing to pay between $50 and $55 a share for the women's retailer, 47% above Friday's closing price of $37.52 at the high end, according to people familiar with the matter.